Franck-Hertz实验建模：源码中魔法数值含义技术问询

Let's break down these mysterious values one by one, grounded in the physics of the Franck-Hertz experiment and common code practices for modeling experimental data:

1. The value 1.3829202595488537 #

This number is almost certainly a fitted coefficient tied to thermal energy scaling, directly linked to the Boltzmann factor that governs electron excitation probability in the experiment. Here's the breakdown:

• In the Franck-Hertz experiment, electron current depends on how likely electrons are to lose energy to mercury atoms—a probability described by the Boltzmann distribution, often modeled with a term like exp(-ΔE/(kT)) (where ΔE is mercury's first excitation energy, k is Boltzmann's constant, and T is the mercury vapor temperature).
• This specific value is very close to 1/0.723 ≈ 1.383, which suggests it’s likely a normalized version of e/(kT) (combining electron charge e with thermal energy kT) adjusted to match real experimental data. Real mercury vapor in the experiment runs at ~100-200°C (373-473K), corresponding to kT/e ≈ 0.03-0.04 eV, so this scaled value implies the author used a simplified model to match the shape of their observed current-voltage curve rather than literal thermal constants.

2. Values -10.88 and 66.92 #

These are nearly guaranteed to be fitted offset/scaling parameters tailored to account for experimental imperfections:

• -10.88 most likely corrects for a voltage offset, such as contact potential differences between electrodes. These real-world quirks shift the effective acceleration voltage away from the measured value, so this number adjusts the model to align with actual observed curve positioning.
• 66.92 is probably a scaling factor or threshold voltage. It might represent the point where electron energy becomes high enough to consistently excite mercury atoms (triggering the first sharp current drop) or a scaling term to match the amplitude of the author’s experimental current readings.

Key Context: Empirical Fitting in Experimental Models #

"Magic numbers" like these are standard in physics experiment code when authors fit theoretical models to real lab data. The creator likely took their own Franck-Hertz measurements, then used a curve-fitting tool (like scipy.optimize.curve_fit in Python) to find these coefficients that best matched their observed current-voltage curve.

To confirm their roles, you can:

• Tweak each value and observe how the output curve changes: adjusting 1.3829... will alter the steepness of the exponential decay, -10.88 shifts the curve left/right, and 66.92 modifies peak positions or amplitude.
• Replace them with values tailored to your own setup (e.g., use kT/e ≈ 0.035 eV for 400K vapor, adjust offsets based on your electrode contact potentials) to adapt the model to your experiment.

内容的提问来源于stack exchange，提问作者Павел Михаловский